The purpose of this experiment is analyze and understand the concept for the time interval between two events with different frame of reference and with the concept of simultaneity. Furthermore, this experiment will also analyze the diffreence between two points when each of them depends on the different frame of reference.
The concept of time interval was summed up by the followed equation for time dilation:
∆t = γ∆t0,
where ∆t0 represents the time of the observer at rest, which is also the known as the rest frame of this observer. ∆t , on the other hand, is known as the frame which is moving with a constant speed relative to the rest frame mentioned earlier.
The above equation shows us that ∆t is always larger than ∆t0 since speed u can never be larger than the speed of light.
The concept of length constration is explained by the following equation:
l= γ/l0
where, the γ is the same symbol used for the time dilation. Therefore, with the same concept that the speend of light is alwasy faster than the moving speed, the lenght of the stationary frame l0 , which is also known as the rest frame is alwasy shorter than the lenght of the moving frame l, and that is why the equation is used for determining the length constration.
In order to fully undertand the concept behind its equation, the online source , Active Physics would be used to see and prove how the time and the lenght changes with the constant speed applied in different frame of reference.
Pictures for Time Interval:
The left picture shows the stationary frame of reference.
The right picture shows the moving frame of reference.
Image represents the time interval when γ = 1.40
Image represents the time interval when γ = 1.30
Image represents the time interval when γ = 1.20
Analysis&Conclusion:
The above three images has different γ values, since γ depends on the ratio of
u2/c2, therefore, when the values γ is larger, this means u, the speed would be faster. Therefore, with equation ∆t = γ∆t0, it shows that when γ is larger, the time taken for the light to travel back is longer. The three above images proves the equation, the time tacken for value γ 1.40, 1.30,1.10 are 9.34 (μs), 8.67(μs), and 7.33(μs). On the other hand, the time taken by the stationary clock is same for all three cases, which is 6.67 (μs) since the position where the light leaves is the same as the position when the light reaches back. Therefore,the round-trip distance for the stationary clock will be 2d, and the round-trip ditance for the moving clock, on the other hand, is denoted as the radical of (d2+ ((u * ∆t )/2)2 .We notice that the round-trip distance for the moving clock will get longer with the increasing of velocity. Hence it also shows that the round-trip distance would be propotional to the time interval.
Pictures for Time Interval:
The top picture shows the stationary frame of reference.
The bottom picture shows the moving frame of reference.
Image represents the interval when γ = 1.40
Image represents the interval when γ = 1.30
Image represents the interval when γ = 1.40
The above three images has different γ values, since γ depends on the ratio of
u2/c2, and since the equation l= γ/l0 , it shows that the length contraction would be the reciprocal of the proper lentgh. Therefore, when the values γ is larger, which also means u, the speed would be faster. Therefore, with the constanct length of the stationany clock, it shows that the constraction length will get shorter as the velocity of the light beam decreases. This result is also proved by the above three images, where the value of γ is 1.40, 1.30, and 1.10, the constraction lenght follows as 714(m), 769(m), and 909(m). These values show that the value γ is recipricol to the length at the moving frame of inference. On the other hand, the time taken at the frame of inference for the stationary clock is all 6.67 (μs) for each case, and the proper lenght for each case for the stationary clock is all 1000m. Furthermore, by applying the equation of ∆t = γ∆t0, it shows that it shares the same concept of time interval when it was applied for the time interval tacken at different frames of inference mentioned earlier in this experiment.
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